Question

problem 8: (first taught in lesson 26) determine whether this definition passes the reversibility test by writing its converse and determining whether the converse is true. then, select your answer. parallel lines are lines that lie in the same plane and never intersect.

Explanation:

Step1: Identify the original statement

The original statement is: "If two lines are parallel, then they lie in the same plane and never intersect." (In logical form: Let \( p \): two lines are parallel; \( q \): two lines lie in the same plane and never intersect. So \( p \implies q \))

Step2: Write the converse

The converse of \( p \implies q \) is \( q \implies p \). So the converse statement is: "If two lines lie in the same plane and never intersect, then they are parallel."

Step3: Determine if the converse is true

By the definition of parallel lines in Euclidean geometry, lines in the same plane that do not intersect are parallel. So the converse is true. Since the converse is true, the original definition passes the reversibility test.

Answer:

The definition passes the reversibility test (the converse is true).